Question: Find the greatest common factor of $10, 30,$ and $45$.
The greatest common factor (GCF) is the largest number that is a factor of $10, 30,$ and $45$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}10 &=2\cdot5\\\\\\\\ 30&=2\cdot3\cdot5\\\\\\\\ 45&=3\cdot3\cdot5 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}10 &=2\cdot5\\\\\\\\ 30&=2\cdot3\cdot5\\\\\\\\ 45&=3\cdot3\cdot5 \end{aligned}$ Each number shares the factor ${5},$ so the GCF is ${5}$. The greatest common factor of $10, 30,$ and $45$ is $5$.